The Symplectic Sum Formula for Gromov-Witten Invariants
Eleny-Nicoleta Ionel, Thomas H. Parker
TL;DR
This paper derives a formula linking Gromov-Witten invariants of a symplectic sum to the relative invariants of the summand manifolds, with applications to enumerative geometry.
Contribution
It introduces the symplectic sum formula for Gromov-Witten invariants, connecting invariants of summed manifolds to those of the original components.
Findings
Established the symplectic sum formula for Gromov-Witten invariants.
Provided applications to enumerative geometry.
Connected relative invariants to global invariants of symplectic sums.
Abstract
In the symplectic category there is a `connect sum' operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z=X#Y in terms of the relative GW invariants of X and Y. Several applications to enumerative geometry are given.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry